Complexity of optimizing over the integers

In the first part of this paper, we present a unified framework for analyzing algorithmic complexity any optimization problem, whether it be continuous or discrete in nature. This helps to formalize notions like “input”, “size” and “complexity” context general mathematical optimization, avoiding dependent definitions which is one sources difference treatment within optimization. second employ language developed study information theoretic mixed-integer convex contains as special case on hand pure integer other. We strive maximum possible generality our exposition. hope that paper material both optimizers find new interesting, even though almost all presented common knowledge other community. see main merit bringing together under unifying umbrella with will act yet another catalyst more interaction across continuous-discrete divide. fact, motivation behind Part I provide communities.